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Palindromic Merlon Primes (PMP's)
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121141151171181
313323343353373
383717727747757
787919929949959
979989   


Palindromic Merlon Primes

Palindromic Merlon Primes (or PMP's for short) are numbers that
are (probable) primes, palindromic in base 10, and consisting of one central digit
(hereby named as a merlon_digit) surrounded by two symmetrical crennelations
with same digits different from the central merlon_digit and finally bordered left
and right by that same central merlon_digit. E.g.

3223223
 31111111111111111311111111111111113

From these examples you will understand the naming of these kind of palindromic primes Visualising merlons

Some links where PMP's are discussed ¬
Liczby pierwsze o szczególnym rozmieszczeniu cyfr by Andrzej Nowicki
    Translated in Dutch “Priemgetallen met een speciale rangschikking van cijfers”
    Translated in English “Prime numbers with a special arrangement of digits”
1221221 from the site 'Darkbyte'
3223223 from Prime Curios!

In case one should discover more sources I will be most happy
to add them to the list. Just let me know.

PMP's sorted by length

Some combinations can never produce primes since
these are always divisible by 3.
1(0)w1(0)w1
1(3)w1(3)w1
1(6)w1(6)w1
1(9)w1(9)w1
3(0)w3(0)w3
3(6)w3(6)w3
3(9)w3(9)w3
7(0)w7(0)w7
7(3)w7(3)w7
7(6)w7(6)w7
7(9)w7(9)w7
9(0)w9(0)w9
9(3)w9(3)w9
9(6)w9(6)w9


PMP Factorization Projects

( n = 2 * w + 3 )

PMP (Palindromic Merlon Primes) reference files.
Members can be prime.
All files maintained by Patrick De Geest.
1(2)w1(2)w1 = 2*(10n–1)/9 – 10n-1 – 10(n-1)/2 – 1 facpmp121.htm  Free to factor    16 remaining  
1(4)w1(4)w1 = 4*(10n–1)/9 – 3*10n-1 – 3*10(n-1)/2 – 3 facpmp141.htm  Free to factor    12 remaining  
1(5)w1(5)w1 = 5*(10n–1)/9 – 4*10n-1 – 4*10(n-1)/2 – 4 facpmp151.htm  Free to factor    12 remaining  
1(7)w1(7)w1 = 7*(10n–1)/9 – 6*10n-1 – 6*10(n-1)/2 – 6 facpmp171.htm  Free to factor    15 remaining  
1(8)w1(8)w1 = 8*(10n–1)/9 – 7*10n-1 – 7*10(n-1)/2 – 7 facpmp181.htm  Free to factor    20 remaining  
3(1)w3(1)w3 = 3*(10n–1)/9 + 2*10n-1 + 2*10(n-1)/2 + 2 facpmp313.htm  Free to factor    15 remaining  
3(2)w3(2)w3 = 2*(10n–1)/9 + 10n-1 + 10(n-1)/2 + 1 facpmp323.htm  Free to factor    13 remaining  
3(4)w3(4)w3 = 4*(10n–1)/9 – 10n-1 – 10(n-1)/2 – 1 facpmp343.htm  Free to factor    13 remaining  
3(5)w3(5)w3 = 5*(10n–1)/9 – 2*10n-1 – 2*10(n-1)/2 – 2 facpmp353.htm  Free to factor    24 remaining  
3(7)w3(7)w3 = 7*(10n–1)/9 – 4*10n-1 – 4*10(n-1)/2 – 4 facpmp373.htm  Free to factor    11 remaining  
3(8)w3(8)w3 = 8*(10n–1)/9 – 5*10n-1 – 5*10(n-1)/2 – 5 facpmp383.htm  Free to factor    15 remaining  
7(1)w7(1)w7 = (10n–1)/9 + 6*10n-1 + 6*10(n-1)/2 + 6 facpmp717.htm  Free to factor    17 remaining  
7(2)w7(2)w7 = 2*(10n–1)/9 + 5*10n-1 + 5*10(n-1)/2 + 5 facpmp727.htm  Free to factor    14 remaining  
7(4)w7(4)w7 = 4*(10n–1)/9 + 3*10n-1 + 3*10(n-1)/2 + 3 facpmp747.htm  Free to factor    16 remaining  
7(5)w7(5)w7 = 5*(10n–1)/9 + 2*10n-1 + 2*10(n-1)/2 + 2 facpmp757.htm  Free to factor    19 remaining  
7(8)w7(8)w7 = 8*(10n–1)/9 – 10n-1 – 10(n-1)/2 + 2 facpmp787.htm  Free to factor    16 remaining  
9(1)w9(1)w9 = (10n–1)/9 + 8*10n-1 + 8*10(n-1)/2 + 8 facpmp919.htm  Free to factor    13 remaining  
9(2)w9(2)w9 = 2*(10n–1)/9 + 7*10n-1 + 7*10(n-1)/2 + 7 facpmp929.htm  Free to factor    13 remaining  
9(4)w9(4)w9 = 4*(10n–1)/9 + 5*10n-1 + 5*10(n-1)/2 + 5 facpmp949.htm  Free to factor    17 remaining  
9(5)w9(5)w9 = 5*(10n–1)/9 + 4*10n-1 + 4*10(n-1)/2 + 4 facpmp959.htm  Free to factor    19 remaining  
9(7)w9(7)w9 = 7*(10n–1)/9 + 2*10n-1 + 2*10(n-1)/2 + 2 facpmp979.htm  Free to factor    13 remaining  
9(8)w9(8)w9 = 8*(10n–1)/9 + 10n-1 + 10(n-1)/2 + 1 facpmp989.htm  Free to factor    20 remaining  
PMP (Palindromic Merlon Primes) reference files.
Members (n>1) are always composite.
All files maintained by Patrick De Geest  [ Factorization Files Under Construction ]
1(0)w1(0)w1 = 10n + 10n/2 + 1 → (n even) facpmp101.htm  All factored (w ⩽ 100) 
1(3)w1(3)w1 = 3*(10n–1)/9 – 2.10n-1 – 2.10(n-1)/2 – 2 facpmp131.htm  Free to factor    13 remaining  
1(6)w1(6)w1 = 6*(10n–1)/9 – 5.10n-1 – 5.10(n-1)/2 – 5 facpmp161.htm  Free to factor    12 remaining  
1(9)w1(9)w1 = 9*(10n–1)/9 – 8.10n-1 – 8.10(n-1)/2 – 8 facpmp191.htm  Free to factor    7 remaining  
2(1)w2(1)w2 = (10n–1)/9 + 10n-1 + 10(n-1)/2 + 1 facpmp212.htm  Free to factor    7 remaining  
2(3)w2(3)w2 = 3*(10n–1)/9 – 10n-1 – 10(n-1)/2 – 1 facpmp232.htm  All factored (w ⩽ 100) 
2(5)w2(5)w2 = 5*(10n–1)/9 – 3*10n-1 – 3*10(n-1)/2 – 3 facpmp252.htm  Free to factor    9 remaining  
2(7)w2(7)w2 = 7*(10n–1)/9 – 5*10n-1 – 5*10(n-1)/2 – 5 facpmp272.htm  All factored (w ⩽ 100) 
2(9)w2(9)w2 = 9*(10n–1)/9 – 7*10n-1 – 7*10(n-1)/2 – 7 facpmp292.htm  Free to factor    13 remaining  
4(1)w4(1)w4 = (10n–1)/9 + 3*10n-1 + 3*10(n-1)/2 + 3 facpmp414.htm  Free to factor    12 remaining  
4(3)w4(3)w4 = 3*(10n–1)/9 + 10n-1 + 10(n-1)/2 + 1 facpmp434.htm  Free to factor    11 remaining  
4(5)w4(5)w4 = 5*(10n–1)/9 – 10n-1 – 10(n-1)/2 – 1 facpmp454.htm  Free to factor    13 remaining  
4(7)w4(7)w4 = 7*(10n–1)/9 – 3*10n-1 – 3*10(n-1)/2 – 3 facpmp474.htm  Free to factor    10 remaining  
4(9)w4(9)w4 = 9*(10n–1)/9 – 5*10n-1 – 5*10(n-1)/2 – 5 facpmp494.htm  Free to factor    11 remaining  
5(1)w5(1)w5 = (10n–1)/9 + 4*10n-1 + 4*10(n-1)/2 + 4 facpmp515.htm  
5(2)w5(2)w5 = 2*(10n–1)/9 + 3*10n-1 + 3*10(n-1)/2 + 3 facpmp525.htm  
5(3)w5(3)w5 = 3*(10n–1)/9 + 2*10n-1 + 2*10(n-1)/2 + 2 facpmp535.htm  
5(4)w5(4)w5 = 4*(10n–1)/9 + 10n-1 + 10(n-1)/2 + 1 facpmp545.htm  
5(6)w5(6)w5 = 6*(10n–1)/9 – 10n-1 – 10(n-1)/2 – 1 facpmp565.htm  
5(7)w5(7)w5 = 7*(10n–1)/9 – 2*10n-1 – 2*10(n-1)/2 – 2 facpmp575.htm  
5(8)w5(8)w5 = 8*(10n–1)/9 – 3*10n-1 – 3*10(n-1)/2 – 3 facpmp585.htm  
5(9)w5(9)w5 = 9*(10n–1)/9 – 4*10n-1 – 4*10(n-1)/2 – 4 facpmp595.htm  
6(1)w6(1)w6 = (10n–1)/9 + 5*10n-1 + 5*10(n-1)/2 + 5 facpmp616.htm  
6(5)w6(5)w6 = 5*(10n–1)/9 + 10n-1 + 10(n-1)/2 + 1 facpmp656.htm  
6(7)w6(7)w6 = 7*(10n–1)/9 – 10n-1 – 10(n-1)/2 – 1 facpmp676.htm  
7(3)w7(3)w7 = 3*(10n–1)/9 + 4*10n-1 + 4*10(n-1)/2 + 4 facpmp737.htm  
7(6)w7(6)w7 = 6*(10n–1)/9 + 10n-1 + 10(n-1)/2 + 1 facpmp767.htm  
7(9)w7(9)w7 = 9*(10n–1)/9 – 2*10n-1 – 2*10(n-1)/2 – 2 facpmp797.htm  
8(1)w8(1)w8 = (10n–1)/9 + 7*10n-1 + 7*10(n-1)/2 + 7 facpmp818.htm  
8(3)w8(3)w8 = 3*(10n–1)/9 + 5*10n-1 + 5*10(n-1)/2 + 5 facpmp838.htm  
8(5)w8(5)w8 = 5*(10n–1)/9 + 3*10n-1 + 3*10(n-1)/2 + 3 facpmp858.htm  
8(7)w8(7)w8 = 7*(10n–1)/9 + 10n-1 + 10(n-1)/2 + 1 facpmp878.htm  
8(9)w8(9)w8 = 9*(10n–1)/9 – 10n-1 – 10(n-1)/2 – 1 facpmp898.htm  

[ February 4, 2023 ]
Chen Xinyao informs me that
https://www.alpertron.com.ar/MODFERM.HTM is the factorization of the PMPs 1(0^^w)1(0^^w)1 in base 2.

Following condition must be imposed that gcd(A,B) = 1 (in Factorization of ABB...BBABB...BBA), i.e. A and B are coprime, since if A and B have a common factor > 1, then we can divide this
factor from the number, e.g. factor 6999...9996999...9996 is equivalent to factor 2333...3332333...3332.

[ April 18, 2023 ]
Chen Xinyao informs me that
some PMPs have algebraic factors: (n=w+1)

2(3^^w)2(3^^w)2 3*(10^(2*n+1)-1)/9-10^(2*n)-10^n-1 = ((2^n*5^n-1)*(7*2^n*5^n+4))/3 = (1^^n) * (7(0^^(n-1)4) * 3
2(7^^w)2(7^^w)2 7*(10^(2*n+1)-1)/9-5*10^(2*n)-5*10^n-5 = ((2^n*5^(n+1)-13)*(2^n*5^(n+1)+4))/9 = 4(9^^(n-2))87 * 5(0^^(n-1))4 / 9

I have checked all combinations of PMP, only 2333...3332333...3332 and 2777...7772777...7772 have algebraic factorization.

Thus link to Kamada's pages factorization of (1^^n), factorization of 7(0^^n)4, factorization of 2*5(0^^n)4
Unfortunately, Kamada's page has no factorization of 4(9^^n)87 or any related numbers since it only has
(x^^n), (x^^n)y, x(y^^n), (x^^n)yx, xy(x^^n), x(y^^n)x, x(y^^n)z, and (x^^n)y(x^^n).

Also 5*10^n-13 (or 4(9^^(n-2))87) is already fully factored for all n<137,
see http://factordb.com/index.php?query=5*10%5En-13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show


The “PMP” Table


The reference table for
Palindromic Merlon Primes
This collection is complete for
probable primes up to 50000
digits and for proven
primes up to  3500  digits.
PDG = Patrick De Geest
PMPFormula
blue exp = # of digits
Accolades = prime exp		WhoWhenStatusOutput
Logs
 ¬ 
   n ⩾ 50011 (PDG, September 27, 2022)
1(2)21(2)21 2*(10{7}–1)/9 – 106 – 103 – 1 PDGNov 12 2011PRIME View
1(2)41(2)41 2*(10{11}–1)/9 – 1010 – 105 – 1 PDGNov 12 2011PRIME View
1(2)111(2)111 2*(1025–1)/9 – 1024 – 1012 – 1 PDGNov 12 2011PRIME View
1(2)23921(2)23921 2*(10{4787}–1)/9 – 104786 – 102393 – 1 PDGNov 12 2011RECORD
PROVEN
PRIME		 View
1(2)188141(2)188141 2*(1037631–1)/9 – 1037630 – 1018815 – 1 PDGSep 27 2022PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 50191 (PDG, September 28, 2022)
1(4)441(4)441 4*(1091–1)/9 – 3*1090 – 3*1045 – 3 PDGNov 12 2011PRIME View
1(4)641(4)641 4*(10{131}–1)/9 – 3*10130 – 3*1065 – 3 PDGNov 12 2011PRIME View
1(4)91491(4)91491 4*(10{18301}–1)/9 – 3*1018300 – 3*109150 – 3 PDGNov 12 2011PROBABLE
PRIME		 View
1(4)228261(4)228261 4*(1045655–1)/9 – 3*1045654 – 3*1022827 – 3 PDGSep 28 2022PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 53947 (PDG, September 28, 2022)
1(5)21(5)21 5*(10{7}–1)/9 – 4*106 – 4*103 – 4 PDGNov 12 2011PRIME View
1(5)81(5)81 5*(10{19}–1)/9 – 4*1018 – 4*109 – 4 PDGNov 12 2011PRIME View
1(5)321(5)321 5*(10{67}–1)/9 – 4*1066 – 4*1033 – 4 PDGNov 12 2011PRIME View
1(5)1281(5)1281 5*(10259–1)/9 – 4*10258 – 4*10129 – 4 PDGNov 12 2011PRIME View
1(5)4941(5)4941 5*(10{991}–1)/9 – 4*10990 – 4*10495 – 4 PDGNov 12 2011PRIME View
1(5)42611(5)42611 5*(108525–1)/9 – 4*108524 – 4*104262 – 4 PDGNov 12 2011PROBABLE
PRIME		 View
1(5)137651(5)137651 5*(1027533–1)/9 – 4*1027532 – 4*1013766 – 4 PDGSep 28 2022PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 56095 (PDG, September 29, 2022)
1(7)41(7)41 7*(10{11}–1)/9 – 6*1010 – 6*105 – 6 PDGNov 12 2011PRIME View
1(7)221(7)221 7*(10{47}–1)/9 – 6*1046 – 6*1023 – 6 PDGNov 12 2011PRIME View
1(7)3161(7)3161 7*(10635–1)/9 – 6*10634 – 6*10317 – 6 PDGNov 12 2011PRIME View
1(7)4421(7)4421 7*(10{887}–1)/9 – 6*10886 – 6*10443 – 6 PDGNov 12 2011PRIME View
 ¬ 
   n ⩾ 58103 (PDG, September 29, 2022)
1(8)11(8)11 8*(10{5}–1)/9 – 7*104 – 7*102 – 7 PDGNov 12 2011PRIME View
1(8)21(8)21 8*(10{7}–1)/9 – 7*106 – 7*103 – 7 PDGNov 12 2011PRIME View
1(8)1451(8)1451 8*(10{293}–1)/9 – 7*10292 – 7*10146 – 7 PDGNov 12 2011PRIME View
1(8)2541(8)2541 8*(10511–1)/9 – 7*10510 – 7*10255 – 7 PDGNov 12 2011PRIME View
1(8)16271(8)16271 8*(10{3257}–1)/9 – 7*103256 – 7*101628 – 7 PDGNov 12 2011PRIME View
1(8)18131(8)18131 8*(103629–1)/9 – 7*103628 – 7*101814 – 7 PDGNov 12 2011PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 53315 (PDG, September 30, 2022)
3(1)163(1)163 (1035–1)/9 + 2*1034 + 2*1017 + 2 PDGNov 12 2011PRIME View
3(1)433(1)433 (10{89}–1)/9 + 2*1088 + 2*1044 + 2 PDGNov 12 2011PRIME View
3(1)863(1)863 (10175–1)/9 + 2*10174 + 2*1087 + 2 PDGNov 12 2011PRIME View
3(1)11533(1)11533 (10{2309}–1)/9 + 2*102308 + 2*101154 + 2 PDGNov 12 2011PRIME View
 ¬ 
   n ⩾ 50821 (PDG, October 1, 2022)
3(2)13(2)13 2*(10{5}–1)/9 + 104 + 102 + 1 PDGNov 12 2011PRIME View
3(2)23(2)23 2*(10{7}–1)/9 + 106 + 103 + 1 PDGNov 12 2011PRIME View
3(2)53(2)53 2*(10{13}–1)/9 + 1012 + 106 + 1 PDGNov 12 2011PRIME View
3(2)19033(2)19033 2*(10{3809}–1)/9 + 103808 + 101904 + 1 PDGNov 12 2011PROBABLE
PRIME		 View
3(2)29533(2)29533 2*(105909–1)/9 + 105908 + 102954 + 1 PDGNov 12 2011PROBABLE
PRIME		 View
3(2)34133(2)34133 2*(10{6829}–1)/9 + 106828 + 103414 + 1 PDGNov 12 2011PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 50189 (PDG, October 2, 2022)
3(4)23(4)23 4*(10{7}–1)/9 – 106 – 103 – 1 PDGDec 27 2012PRIME View
3(4)43(4)43 4*(10{11}–1)/9 – 1010 – 105 – 1 PDGNov 12 2011PRIME View
3(4)73(4)73 4*(10{17}–1)/9 – 1016 – 108 – 1 PDGNov 12 2011PRIME View
3(4)223(4)223 4*(10{47}–1)/9 – 1046 – 1023 – 1 PDGNov 12 2011PRIME View
3(4)263(4)263 4*(1055–1)/9 – 1054 – 1027 – 1 PDGNov 12 2011PRIME View
3(4)1823(4)1823 4*(10{367}–1)/9 – 10366 – 10183 – 1 PDGNov 12 2011PRIME View
3(4)2053(4)2053 4*(10413–1)/9 – 10412 – 10206 – 1 PDGNov 12 2011PRIME View
3(4)4763(4)4763 4*(10955–1)/9 – 10954 – 10477 – 1 PDGNov 12 2011PRIME View
3(4)13193(4)13193 4*(102641–1)/9 – 102640 – 101320 – 1 PDGNov 12 2011PRIME View
3(4)127423(4)127423 4*(1025487–1)/9 – 1025486 – 1012743 – 1 PDGOct 1 2022PROBABLE
PRIME		 View
3(4)172433(4)172433 4*(1034489–1)/9 – 1034488 – 1017244 – 1 PDGOct 1 2022PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 50657 (PDG, October 2, 2022)
3(5)13(5)13 5*(10{5}–1)/9 – 2*104 – 2*102 – 2 PDGNov 12 2011PRIME View
3(5)23(5)23 5*(10{7}–1)/9 – 2*106 – 2*103 – 2 PDGNov 12 2011PRIME View
3(5)173(5)173 5*(10{37}–1)/9 – 2*1036 – 2*1018 – 2 PDGNov 12 2011PRIME View
3(5)203(5)203 5*(10{43}–1)/9 – 2*1042 – 2*1021 – 2 PDGNov 12 2011PRIME View
3(5)263(5)263 5*(1055–1)/9 – 2*1054 – 2*1027 – 2 PDGNov 12 2011PRIME View
3(5)1573(5)1573 5*(10{317}–1)/9 – 2*10316 – 2*10158 – 2 PDGNov 12 2011PRIME View
3(5)6143(5)6143 5*(10{1231}–1)/9 – 2*101230 – 2*10615 – 2 PDGNov 12 2011PRIME View
3(5)8333(5)8333 5*(10{1669}–1)/9 – 2*101668 – 2*10834 – 2 PDGNov 12 2011PRIME View
3(5)33613(5)33613 5*(106725–1)/9 – 2*106724 – 2*103362 – 2 PDGNov 12 2011PROBABLE
PRIME		 View
3(5)36313(5)36313 5*(107265–1)/9 – 2*107264 – 2*103632 – 2 PDGNov 12 2011PROBABLE
PRIME		 View
3(5)38443(5)38443 5*(10{7691}–1)/9 – 2*107690 – 2*103845 – 2 PDGNov 12 2011PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 55429 (PDG, October 3, 2022)
3(7)23(7)23 7*(10{7}–1)/9 – 4*106 – 4*103 – 4 PDGNov 12 2011PRIME View
3(7)43(7)43 7*(10{11}–1)/9 – 4*1010 – 4*105 – 4 PDGNov 12 2011PRIME View
3(7)473(7)473 7*(10{97}–1)/9 – 4*1096 – 4*1048 – 4 PDGNov 12 2011PRIME View
3(7)593(7)593 7*(10121–1)/9 – 4*10120 – 4*1060 – 4 PDGNov 12 2011PRIME View
3(7)703(7)703 7*(10143–1)/9 – 4*10142 – 4*1071 – 4 PDGNov 12 2011PRIME View
3(7)1223(7)1223 7*(10247–1)/9 – 4*10246 – 4*10123 – 4 PDGNov 12 2011PRIME View
3(7)1283(7)1283 7*(10259–1)/9 – 4*10258 – 4*10129 – 4 PDGNov 12 2011PRIME View
3(7)60943(7)60943 7*(1012191–1)/9 – 4*1012190 – 4*106095 – 4 PDGDec 4 2011PROBABLE
PRIME		 View
3(7)85243(7)85243 7*(1017051–1)/9 – 4*1017050 – 4*108525 – 4 PDGDec 4 2011PROBABLE
PRIME		 View
3(7)189893(7)189893 7*(1037981–1)/9 – 4*1037980 – 4*1018990 – 4 PDGOct 3 2022PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 50417 (PDG, October 4, 2022)
3(8)83(8)83 8*(10{19}–1)/9 – 5*1018 – 5*109 – 5 PDGNov 12 2011PRIME View
3(8)103(8)103 8*(10{23}–1)/9 – 5*1022 – 5*1011 – 5 PDGNov 12 2011PRIME View
3(8)143(8)143 8*(10{31}–1)/9 – 5*1030 – 5*1015 – 5 PDGNov 12 2011PRIME View
3(8)673(8)673 8*(10{137}–1)/9 – 5*10136 – 5*1068 – 5 PDGNov 12 2011PRIME View
3(8)3643(8)3643 8*(10731–1)/9 – 5*10730 – 5*10365 – 5 PDGNov 12 2011PRIME View
3(8)5783(8)5783 8*(101159–1)/9 – 5*101158 – 5*10579 – 5 PDGNov 12 2011PRIME View
3(8)8483(8)8483 8*(10{1699}–1)/9 – 5*101698 – 5*10849 – 5 PDGNov 12 2011PRIME View
3(8)30763(8)30763 8*(106155–1)/9 – 5*106154 – 5*103077 – 5 PDGNov 12 2011PROBABLE
PRIME		 View
3(8)78403(8)78403 8*(10{15683}–1)/9 – 5*1015682 – 5*107841 – 5 PDGDec 5 2011PROBABLE
PRIME		 View
3(8)142063(8)142063 8*(1028415–1)/9 – 5*1028414 – 5*1014207 – 5 PDGOct 3 2022PROBABLE
PRIME		 View
3(8)193993(8)193993 8*(1038801–1)/9 – 5*1038800 – 5*1019400 – 5 PDGOct 4 2022PROBABLE
PRIME		 View
3(8)233963(8)233963 8*(1046795–1)/9 – 5*1046794 – 5*1023397 – 5 PDGOct 4 2022PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 50681 (PDG, October 4, 2022)
7(1)557(1)557 (10{113}–1)/9 + 6*10112 + 6*1056 + 6 PDGNov 12 2011PRIME View
 ¬ 
   n ⩾ 51193 (PDG, October 5, 2022)
7(2)17(2)17 2*(10{5}–1)/9 + 5*104 + 5*102 + 5 PDGNov 12 2011PRIME View
7(2)47(2)47 2*(10{11}–1)/9 + 5*1010 + 5*105 + 5 PDGNov 12 2011PRIME View
7(2)77(2)77 2*(10{17}–1)/9 + 5*1016 + 5*108 + 5 PDGNov 12 2011PRIME View
7(2)227(2)227 2*(10{47}–1)/9 + 5*1046 + 5*1023 + 5 PDGNov 12 2011PRIME View
7(2)297(2)297 2*(10{61}–1)/9 + 5*1060 + 5*1030 + 5 PDGNov 12 2011PRIME View
7(2)497(2)497 2*(10{101}–1)/9 + 5*10100 + 5*1050 + 5 PDGNov 12 2011PRIME View
7(2)737(2)737 2*(10{149}–1)/9 + 5*10148 + 5*1074 + 5 PDGNov 12 2011PRIME View
7(2)837(2)837 2*(10169–1)/9 + 5*10168 + 5*1084 + 5 PDGNov 12 2011PRIME View
7(2)1187(2)1187 2*(10{239}–1)/9 + 5*10238 + 5*10119 + 5 PDGNov 12 2011PRIME View
7(2)2417(2)2417 2*(10485–1)/9 + 5*10484 + 5*10242 + 5 PDGNov 12 2011PRIME View
 ¬ 
   n ⩾ 51035 (PDG, October 5, 2022)
7(4)17(4)17 4*(10{5}–1)/9 + 3*104 + 3*102 + 3 PDGNov 12 2011PRIME View
7(4)1217(4)1217 4*(10245–1)/9 + 3*10244 + 3*10122 + 3 PDGNov 12 2011PRIME View
7(4)5207(4)5207 4*(101043–1)/9 + 3*101042 + 3*10521 + 3 PDGNov 12 2011PRIME View
7(4)12647(4)12647 4*(10{2531}–1)/9 + 3*102530 + 3*101265 + 3 PDGNov 12 2011PRIME View
7(4)17807(4)17807 4*(103563–1)/9 + 3*103562 + 3*101781 + 3 PDGNov 12 2011PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 56255 (PDG, October 5, 2022)
7(5)262727(5)262727 5*(1052547–1)/9 + 2*1052546 + 2*1026273 + 2 PDGNov 12 2011RECORD
PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 53665 (PDG, October 6, 2022)
7(8)17(8)17 8*(10{5}–1)/9 – 104 – 102 – 1 PDGNov 12 2011PRIME View
7(8)47(8)47 8*(10{11}–1)/9 – 1010 – 105 – 1 PDGNov 12 2011PRIME View
7(8)1277(8)1277 8*(10{257}–1)/9 – 10256 – 10128 – 1 PDGNov 12 2011PRIME View
7(8)3297(8)3297 8*(10{661}–1)/9 – 10660 – 10330 – 1 PDGNov 12 2011PRIME View
7(8)8037(8)8037 8*(10{1609}–1)/9 – 101608 – 10804 – 1 PDGNov 12 2011PRIME View
7(8)18407(8)18407 8*(103683–1)/9 – 103682 – 101841 – 1 PDGNov 12 2011PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 50395 (PDG, October 7, 2022)
9(1)49(1)49 (10{11}–1)/9 + 8*1010 + 8*105 + 8 PDGNov 12 2011PRIME View
9(1)79(1)79 (10{17}–1)/9 + 8*1016 + 8*108 + 8 PDGNov 12 2011PRIME View
9(1)299(1)299 (10{61}–1)/9 + 8*1060 + 8*1030 + 8 PDGNov 12 2011PRIME View
9(1)469(1)469 (1095–1)/9 + 8*1094 + 8*1047 + 8 PDGNov 12 2011PRIME View
9(1)589(1)589 (10119–1)/9 + 8*10118 + 8*1059 + 8 PDGNov 12 2011PRIME View
9(1)689(1)689 (10{139}–1)/9 + 8*10138 + 8*1069 + 8 PDGNov 12 2011PRIME View
9(1)839(1)839 (10169–1)/9 + 8*10168 + 8*1084 + 8 PDGNov 12 2011PRIME View
9(1)9559(1)9559 (10{1913}–1)/9 + 8*101912 + 8*10956 + 8 PDGNov 12 2011PRIME View
9(1)11609(1)11609 (102323–1)/9 + 8*102322 + 8*101161 + 8 PDGNov 12 2011PRIME View
9(1)55049(1)55049 (10{11011}–1)/9 + 8*1011010 + 8*105505 + 8 PDGNov 12 2011PROBABLE
PRIME		 View
9(1)62689(1)62689 (10{12539}–1)/9 + 8*1012538 + 8*106269 + 8 PDGNov 12 2011PROBABLE
PRIME		 View
9(1)92909(1)92909 (10{18583}–1)/9 + 8*1018582 + 8*109291 + 8 PDGNov 12 2011PROBABLE
PRIME		 View
9(1)217669(1)217669 (1043535–1)/9 + 8*1043534 + 8*1021767 + 8 PDGOct 6 2022PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 52841 (PDG, October 7, 2022)
9(2)49(2)49 2*(10{11}–1)/9 + 7*1010 + 7*105 + 7 PDGNov 12 2011PRIME View
9(2)89(2)89 2*(10{19}–1)/9 + 7*1018 + 7*109 + 7 PDGNov 12 2011PRIME View
9(2)269(2)269 2*(1055–1)/9 + 7*1054 + 7*1027 + 7 PDGNov 12 2011PRIME View
9(2)2029(2)2029 2*(10407–1)/9 + 7*10406 + 7*10203 + 7 PDGNov 12 2011PRIME View
9(2)20689(2)20689 2*(10{4139}–1)/9 + 7*104138 + 7*102069 + 7 PDGNov 12 2011PROBABLE
PRIME		 View
9(2)63749(2)63749 2*(1012751–1)/9 + 7*1012750 + 7*106375 + 7 PDGNov 12 2011PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 50963 (PDG, October 8, 2022)
9(4)19(4)19 4*(10{5}–1)/9 + 5*104 + 5*102 + 5 PDGNov 12 2011PRIME View
9(4)49(4)49 4*(10{11}–1)/9 + 5*1010 + 5*105 + 5 PDGNov 12 2011PRIME View
9(4)79(4)79 4*(10{17}–1)/9 + 5*1016 + 5*108 + 5 PDGNov 12 2011PRIME View
9(4)209(4)209 4*(10{43}–1)/9 + 5*1042 + 5*1021 + 5 PDGNov 12 2011PRIME View
9(4)5099(4)5099 4*(10{1021}–1)/9 + 5*101020 + 5*10510 + 5 PDGNov 12 2011PRIME View
 ¬ 
   n ⩾ 50461 (PDG, October 8, 2022)
9(5)19(5)19 5*(10{5}–1)/9 + 4*104 + 4*102 + 4 PDGNov 12 2011PRIME View
9(5)389(5)389 5*(10{79}–1)/9 + 4*1078 + 4*1039 + 4 PDGNov 12 2011PRIME View
9(5)1739(5)1739 5*(10{349}–1)/9 + 4*10348 + 4*10174 + 4 PDGNov 12 2011PRIME View
9(5)14939(5)14939 5*(102989–1)/9 + 4*102988 + 4*101494 + 4 PDGNov 12 2011PRIME View
9(5)229909(5)229919 5*(1045983–1)/9 + 4*1045982 + 4*1022991 + 4 PDGOct 8 2022PROBABLE
PRIME		 View
 ¬ 
   n ⩾ 56783 (PDG, October 8, 2022)
9(7)29(7)29 7*(10{7}–1)/9 + 2*106 + 2*103 + 2 PDGNov 12 2011PRIME View
9(7)409(7)409 7*(10{83}–1)/9 + 2*1082 + 2*1041 + 2 PDGNov 12 2011PRIME View
9(7)2989(7)2989 7*(10{599}–1)/9 + 2*10598 + 2*10299 + 2 PDGNov 12 2011PRIME View
 ¬ 
   n ⩾ 52507 (PDG, October 9, 2022)
9(8)29(8)29 8*(10{7}–1)/9 + 106 + 103 + 1 PDGNov 12 2011PRIME View
9(8)49(8)49 8*(10{11}–1)/9 + 1010 + 105 + 1 PDGNov 12 2011PRIME View
9(8)89(8)89 8*(10{19}–1)/9 + 1018 + 109 + 1 PDGNov 12 2011PRIME View
9(8)149(8)149 8*(10{31}–1)/9 + 1030 + 1015 + 1 PDGNov 12 2011PRIME View
9(8)329(8)329 8*(10{67}–1)/9 + 1066 + 1033 + 1 PDGNov 12 2011PRIME View
9(8)569(8)569 8*(10115–1)/9 + 10114 + 1057 + 1 PDGNov 12 2011PRIME View
9(8)3829(8)3829 8*(10767–1)/9 + 10766 + 10383 + 1 PDGNov 12 2011PRIME View


Sources Revealed


Neil Sloane's “Integer Sequences” Encyclopedia can be consulted online :
Neil Sloane's Integer Sequences
Various numbers, primes and palindromic primes are categorised as follows :
%N Merlon numbers. Start is identical to sequence A??????
%N Palindromic merlon primes. under A??????
%N Palindromic merlon primes exist for digitlengths a(n). under A??????
Click here to view some of the author's [P. De Geest] entries to the table.
Click here to view some entries to the table about palindromes.


Prime Curios! - site maintained by G. L. Honaker Jr. and Chris Caldwell
3223223

All probable primes above 10000 digits are also
submitted to the PRP TOP records table maintained by Henri & Renaud Lifchitz.
See : http://www.primenumbers.net/prptop/prptop.php
 

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Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com